320 Prof. W. B. Morton and Mr. L. J. Close on Hertz's 



(2) According to all above-mentioned, this result is equi- 

 valent to the conclusion that the curves of absorption of our 

 dyes are physically simple ones. 



(3) The theory of Einstein is not confirmed, but the devia- 

 tions required by this theory are so small that they exceed 

 only a little the experimental errors, and we are unable to 

 make a definite statement. 



(4) The intensity pf fluorescence radiated by a definite 

 molecular resonator depends only upon the value of the 

 absorbed energy and upon the mechanism of the resonator. 

 In the case of an excitation by a white light we can there- 

 fore write 



J A 



I\.xc.e- Xcd .d\. .... (11) 



Ai 



(5) The result of Nichols and Merritt shows probably 

 only the physical complexity of bands of dyes studied by 

 these authors. 



This work was carried out in the Physics Department of 

 the Scientific Institution of Moscow, to the Director of which, 

 Prof . Dr. P. P. Lasareff, I am much indebted for much valuable 

 help and for his interest during the course of the work. 



XXX. JSotes on Hertz s Tlieory of the Contact of Elastic 

 Bodies. By W. B. Morton, M.A., and L. J. Close, M.A., 

 Queen s University, Belfast *\ 



1. Introduction. 



rTlHE elastic problem of the deformations and stresses 

 I which arise when two bodies, having continuous cur- 

 vature, are pressed together was solved by Hertz f in a 

 classical memoir. "He showed that the area of contact is, in 

 o-eneral ; an ellipse, and that the displacement in the neigh- 

 bourhood of the contact could be expressed by means of 

 potential functions belonging to a certain distribution of 

 surface-density on this ellipse : viz., that reached as the limit 

 of a uniform solid ellipsoid. In view of the complicated 

 nature of the mathematics, Hertz contented himself with 

 establishing some general conclusions and with drawing a 

 diagram of the lines of principal stress which was partly 

 conjectural and which was afterwards found to be erroneous 



* Communicated by the Authors. 



t Hertz, Miscellaneous Papers (Engl, trans.) p. 146. See Love, 

 1 Elasticity' (3rd ed.), p. 191. 



